Question: Simplify the following expression: $\dfrac{45q^4}{60q^5}$ You can assume $q \neq 0$.
Answer: $ \dfrac{45q^4}{60q^5} = \dfrac{45}{60} \cdot \dfrac{q^4}{q^5} $ To simplify $\frac{45}{60}$ , find the greatest common factor (GCD) of $45$ and $60$ $45 = 3 \cdot 3 \cdot 5$ $60 = 2 \cdot 2 \cdot 3 \cdot 5$ $ \mbox{GCD}(45, 60) = 3 \cdot 5 = 15 $ $ \dfrac{45}{60} \cdot \dfrac{q^4}{q^5} = \dfrac{15 \cdot 3}{15 \cdot 4} \cdot \dfrac{q^4}{q^5} $ $\phantom{ \dfrac{45}{60} \cdot \dfrac{4}{5}} = \dfrac{3}{4} \cdot \dfrac{q^4}{q^5} $ $ \dfrac{q^4}{q^5} = \dfrac{q \cdot q \cdot q \cdot q}{q \cdot q \cdot q \cdot q \cdot q} = \dfrac{1}{q} $ $ \dfrac{3}{4} \cdot \dfrac{1}{q} = \dfrac{3}{4q} $